Abstract
Let đ be a triangulated category. When Ï is a functorially finite subcategory of đ, JĂžtrgensen showed that the stable category đ/Ï is a pretriangulated category. A pair (đł, đŽ) of subcategories of đ with Ï â đł â© đŽ gives rise to a pair (đł/Ï, đŽ/Ï) of subcategories of đ/Ï. In this article, we find conditions for (đł/Ï, đŽ/Ï) to be a torsion pair in terms of properties of the pair (đł, đŽ). In particular, we obtain necessary and sufficient conditions for (đł/Ï, đŽ/Ï) to be a torsion pair in the stable category đ/Ï when ÏÏ = Ï, where Ï is the AuslanderâReiten translation.
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